The authors study a simple model of an asset market with informed and non-informed agents. In the absence of non-informed agents, the market becomes information efficient when the number of traders with different private information is large enough. Upon introducing non-informed agents, the authors find that the latter contribute significantly to the trading activity if and only if the market is (nearly) information efficient. This suggests that information efficiency might be a necessary condition for bubble phenomena - induced by the behavior of non-informed traders - or conversely that throwing some sands in the gears of financial markets may curb the occurrence of bubbles.